Advertisements
Advertisements
प्रश्न
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.
Advertisements
उत्तर
In ΔABC,
Since AB = AC
∠C = ∠B ...(angles opposite to the equal sides are equal)
BO and CO are angle bisectors of ∠B and ∠C respectively
Hence, ∠ABO = ∠OBC = ∠BCO = ∠ACO
Join AO to meet BC at D
In ΔABO and ΔACO and
AO = AO
AB = AC
∠C = ∠B =
Therefore, ΔBAO ≅ ΔACO ...(SAS criteria)
Hence, ∠BAO = ∠CAO
⇒ AO bisects angle BAC
In ΔABO and ΔACO
and AB = AC
AO = AO
∠BAD = ∠CAD = ...(proved)
ΔBAO ≅ ΔACO ...(SAS criteria)
Therefore,
BO = CO.
APPEARS IN
संबंधित प्रश्न
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
In ΔPQR ≅ ΔEFD then ED =
In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =
In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
ΔXYZ ≅ ΔLMN
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
